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Let L be the line of intersection of the planes `2x""+""3y""+""z""=""1` and `x""+""3y""+""2z""=""2` . If L makes an angles ` alpha `with the positive x-axis, then cos` alpha ` equals `1/(sqrt(3))` `1/2` 1 `1/(sqrt(2))`

A

`(1)/(2)`

B

1

C

`(1)/(sqrt2)`

D

`(1)/(sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
d
Since line of intersection is perpendicular to both the planes, direction rations of the line of intersection is ltbgt `|[hati,hatj,hatk],[2,3,1],[1,3,2]|=3hati-3hatj+3hatk`
Hence, `cosalpha=(3)/(sqrt(9+9+9))=(1)/(sqrt3)`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. The perpendicular distance between the line vecr = 2hati-2hatj+3hatk+l...

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  3. Let L be the line of intersection of the planes 2x""+""3y""+""z""="...

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  4. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

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  5. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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  7. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

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  8. A line makes an angel theta with each of the x-and z-axes. If the a...

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  9. The shortest distance from the plane 12 x+y+3z=327to the sphere x^2+y^...

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  10. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  11. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4z...

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  12. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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  13. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  14. Two system of rectangular axes have the same origin. IF a plane cuts t...

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  15. Find the equation of a plane which passes through the point (3, 2, 0...

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  16. The dr. of normal to the plane through (1,0,0), (0,1,0) which makes an...

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  17. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

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  18. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

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  19. Distance of the point P(vecc) from the line vecr=veca+lamdavecb is

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  20. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

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